Slice flank steak against the grain into 1/4 inch thick bite-size pieces (tilt the blade of the knife at about a 45 degree angle to get wider cuts). Place steak in a wide, shallow bowl, sprinkle with corn starch, and toss to coat evenly. Set aside for at least 10 minutes so the corn starch sticks to the meat.
Heat 2 teaspoons vegetable oil in a medium saucepan over medium-low heat. Add ginger and garlic and saute, stirring frequently, for 1-2 minutes until fragrant. Add soy sauce and water, then whisk in brown sugar until it dissolves. Increase heat to medium-high, bring to a boil, and cook for 2-3 minutes or until the sauce thickens. Set aside.
In a wok or large skillet, heat enough vegetable oil to cover 1/2 to 3/4 inch of the bottom of the pan over medium heat until hot, but not smoking. Shake excess corn starch off the steak pieces and fry in the hot oil until the edges become crisp and start to brown, about 2 minutes. Do not overcrowd the pan and work in batches, if necessary. Remove meat from the oil with a large slotted spoon and drain on paper towels. Discard excess oil.
Return meat and sauce back to the pan and cook for 2-3 minutes over medium heat, stirring occasionally. Add green onions, stir to coat with sauce, and cook for 1 more minute. Transfer meat and onions to a serving platter, leaving excess sauce in the pan.